PSI - Issue 84

Fulvio Busatta et al. / Procedia Structural Integrity 84 (2026) 797–804

804

Once found the unknowns, the resulting linear combination  k is a new time-series – called cointegration residual – cleaned from trends in the natural frequencies due to EOV. Hence, any anomaly is detected if the cointegration residual deviates from its stationarity as per training period. In Fig. 7, the Upper and Lower Control Limits (UCL, LCL) are set to the 95 th percentile of the cointegration residual  k computed in the training period and anomalies are detected if any observation consistently lies beyond these control limits. Therefore, the cointegration residual is a damage-sensitive feature similarly to the Mahalanobis distance and T 2 -Hotelling statistics built on PCA residuals. Fig. 7 compares the results obtained from the Cointegration and PCA-based control charts mentioned above where the training period is 9 months long (from 31/05/2024 to 28/02/2025), and the remaining testing period is 3 months long (from 01/03/2025 to 31/05/2025). Fig. 7 shows that the 9-month training period is long enough for the Cointegration and Mahalanobis distance PCA-based control charts (outliers =5.2%). Whereas, the PCA-based T 2 -Hotelling control chart needs a longer training period (outliers =42.9%). Moreover, the PCA-based control charts require the manual selection of the number of principal components for the PCA regression and elements in the subgroups to build the T 2 -Hotelling control chart. This adds subjectivity to the method and requires a preliminary sensitivity analysis. Hence, Cointegration seems to be the most promising novelty detection technique. 6. Conclusions The paper presented some selected results from 1-year continuous dynamic monitoring of the PSC box girder bridge named Torrente Reggia bridge. Novelty detection was performed by using different techniques which employed the eleven natural frequencies of the bridge deck that were tracked within the monitoring program. The cointegration residual was computed which inherently removes EOV trends in the natural frequencies. Two well known methods making use of, respectively, the Mahalanobis distance and Hotelling T 2 statistics, and employing the PCA to minimize EOV effects were considered as well. It was shown that control charts resulting from the cointegration and Mahalanobis distance with a short training period (9 months) can perform novelty detection effectively over the 3-month testing period. Conversely, the technique based on the Hotelling T2 statistics needs a longer training period. Hence, the two above mentioned techniques seem more advantageous within the framework of the Italian Guidelines mentioned earlier as bridges with either Medium-High or High-Risk Classification are those mostly monitored so that a robust and early novelty detection is of paramount importance. References Allemang, R.J., Brown, D.L., 1982. A correlation coefficient for modal vector analysis. Proceedings of the 1st International Modal Analysis Conference, Orlando, FL, USA. Cross, E., Koo, K., Brownjohn, J, Worden, K., 2013. Long-term monitoring and data analysis of the Tamar Bridge. Mechanical Systems and Signal Processing 35(1-2), 16–34. CSLP (The Higher Council of Public Works), 2020. Guidelines on Risk Classification and Management, Safety Assessment and Monitoring of Existing Bridges, issued by the Italian Ministry of Infrastructures and Transport with Decree n. 578 on 17/12/2020 (in Italian). García-Macías, E., et al. , 2023. P3P: a software suite for autonomous SHM of bridge networks. J Civil Struct Health Monit 13, 1577–1594. Mahalanobis, PC, On the generalised distance in statistics. Proceedings of the National Institute of Sciences of India, 2(1), 1936, pp. 49–55. Hotelling, H., 1947. Multivariate quality control-illustrated by the air testing of sample bombsights. In: Eisenhart, C. et al. (Eds.). Center, Hampton, 1992. Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12 (2-3), 231–254. Pappa, R., Elliott, K., Schenk, A., 1993. A consistent-mode indicator for the Eigen system realization algorithm. In: NASA technical memorandum 107607, NASA Langley Research. Peeters, B., De Roeck, G., 1999. Reference-based stochastic subspace identification for output-only modal analysis. Mechanical Systems and Signal Processing 13(6), 855–878. Sharma, S., 1995. Applied Multivariate Techniques, John Wiley & Sons, New York. Sohn, H., Farrar, C., Hunter, N., Worden, K., 2001. Structural Health Monitoring Using Statistical Pattern Recognition Techniques. Journal of Dynamic Systems, Measurement, and Control 123(4), 706–711.